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91.
Order statistics from trivariate normal and -distributions in terms of generalized skew-normal and skew- distributions 总被引:1,自引:0,他引:1
We consider here a generalization of the skew-normal distribution, GSN(λ1,λ2,ρ), defined through a standard bivariate normal distribution with correlation ρ, which is a special case of the unified multivariate skew-normal distribution studied recently by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574]. We then present some simple and useful properties of this distribution and also derive its moment generating function in an explicit form. Next, we show that distributions of order statistics from the trivariate normal distribution are mixtures of these generalized skew-normal distributions; thence, using the established properties of the generalized skew-normal distribution, we derive the moment generating functions of order statistics, and also present expressions for means and variances of these order statistics.Next, we introduce a generalized skew-tν distribution, which is a special case of the unified multivariate skew-elliptical distribution presented by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574] and is in fact a three-parameter generalization of Azzalini and Capitanio's [2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J. Roy. Statist. Soc. Ser. B 65, 367–389] univariate skew-tν form. We then use the relationship between the generalized skew-normal and skew-tν distributions to discuss some properties of generalized skew-tν as well as distributions of order statistics from bivariate and trivariate tν distributions. We show that these distributions of order statistics are indeed mixtures of generalized skew-tν distributions, and then use this property to derive explicit expressions for means and variances of these order statistics. 相似文献
92.
The estimation of data transformation is very useful to yield response variables satisfying closely a normal linear model. Generalized linear models enable the fitting of models to a wide range of data types. These models are based on exponential dispersion models. We propose a new class of transformed generalized linear models to extend the Box and Cox models and the generalized linear models. We use the generalized linear model framework to fit these models and discuss maximum likelihood estimation and inference. We give a simple formula to estimate the parameter that index the transformation of the response variable for a subclass of models. We also give a simple formula to estimate the rth moment of the original dependent variable. We explore the possibility of using these models to time series data to extend the generalized autoregressive moving average models discussed by Benjamin et al. [Generalized autoregressive moving average models. J. Amer. Statist. Assoc. 98, 214–223]. The usefulness of these models is illustrated in a simulation study and in applications to three real data sets. 相似文献
93.
The data collection process and the inherent population structure are the main causes for clustered data. The observations in a given cluster are correlated, and the magnitude of such correlation is often measured by the intra-cluster correlation coefficient. The intra-cluster correlation can lead to an inflated size of the standard F test in a linear model. In this paper, we propose a solution to this problem. Unlike previous adjustments, our method does not require estimation of the intra-class correlation, which is problematic especially when the number of clusters is small. Our simulation results show that the new method outperforms the existing methods. 相似文献
94.
Lili Tian Albert Vexler Li Yan Enrique F. Schisterman 《Journal of statistical planning and inference》2009
In many diagnostic studies, multiple diagnostic tests are performed on each subject or multiple disease markers are available. Commonly, the information should be combined to improve the diagnostic accuracy. We consider the problem of comparing the discriminatory abilities between two groups of biomarkers. Specifically, this article focuses on confidence interval estimation of the difference between paired AUCs based on optimally combined markers under the assumption of multivariate normality. Simulation studies demonstrate that the proposed generalized variable approach provides confidence intervals with satisfying coverage probabilities at finite sample sizes. The proposed method can also easily provide P-values for hypothesis testing. Application to analysis of a subset of data from a study on coronary heart disease illustrates the utility of the method in practice. 相似文献
95.
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations 总被引:7,自引:0,他引:7
Håvard Rue Sara Martino Nicolas Chopin 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2009,71(2):319-392
Summary. Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models , where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged. 相似文献
96.
For regression on state and transition probabilities in multi-state models Andersen et al. (Biometrika 90:15–27, 2003) propose
a technique based on jackknife pseudo-values. In this article we analyze the pseudo-values suggested for competing risks models
and prove some conjectures regarding their asymptotics (Klein and Andersen, Biometrics 61:223–229, 2005). The key is a second
order von Mises expansion of the Aalen-Johansen estimator which yields an appropriate representation of the pseudo-values.
The method is illustrated with data from a clinical study on total joint replacement. In the application we consider for comparison
the estimates obtained with the Fine and Gray approach (J Am Stat Assoc 94:496–509, 1999) and also time-dependent solutions
of pseudo-value regression equations. 相似文献
97.
Ørnulf Seippel 《Journal of youth studies》2017,20(4):415-429
Recent decades have seen the growth of various strands of right-wing populist political orientations, where populism and critique of immigration policies have been central. These ideological developments have caused concern for the legitimacy of social and political institutions. The question explored in this paper, based on Norwegian survey data, is ‘Which types of right political orientations exist among young people, and how do these political attitudes affect trust in social and political institutions?’ The results reveal the existence of both a populist ‘new right’ political orientation similar to the ideology of the Progress Party and a nativist ideology. The new right orientation contains two sets of variables: (i) economic liberalism/state scepticism and (ii) nationalist values. For trust in political institutions, the emerging picture is complex because the nationalist dimension of both the populist orientation and the nativist ideological orientation implies a high level of trust in political institutions. To the extent the new right political orientations causes mistrust, it seems to come from the liberal economic, anti-statist values included in this ideology. Based on these findings, future researchers should distinguish more clearly between the ideological dimensions going into populist political right orientations and the relationship between attitudes and more practical implications of such ideologies. 相似文献
98.
In many applications, the clustered count data often contain excess zeros and the zero-inflated generalized Poisson mixed (ZIGPM) regression model may be suitable. However, dispersion in ZIGPM is often treated as fixed unknown parameter, and this assumption may be not appropriate in some situations. In this article, a score test for homogeneity of dispersion parameter in ZIGPM regression model is developed and corresponding test statistic is obtained. Sampling distribution and power of the score test statistic are investigated through Monte Carlo simulation. Finally, results from a biological example illustrate the usefulness of the diagnostic statistic. 相似文献
99.
Marco Barnabani 《统计学通讯:模拟与计算》2017,46(1):331-343
In general, the exact distribution of a convolution of independent gamma random variables is quite complicated and does not admit a closed form. Of all the distributions proposed, the gamma-series representation of Moschopoulos (1985) is relatively simple to implement but for particular combinations of scale and/or shape parameters the computation of the weights of the series can result in complications with too much time consuming to allow a large-scale application. Recently, a compact random parameter representation of the convolution has been proposed by Vellaisamy and Upadhye (2009) and it allows to give an exact interpretation to the weights of the series. They describe an infinite discrete probability distribution. This result suggested to approximate Moschopoulos’s expression looking for an approximating theoretical discrete distribution for the weights of the series. More precisely, we propose a general negative binomial distribution. The result is an “excellent” approximation, fast and simple to implement for any parameter combination. 相似文献
100.
The ordinary-G class of distributions is defined to have the cumulative distribution function (cdf) as the value of the cdf of the ordinary distribution F whose range is the unit interval at G, that is, F(G), and it generalizes the ordinary distribution. In this work, we consider the standard two-sided power distribution to define other classes like the beta-G and the Kumaraswamy-G classes. We extend the idea of two-sidedness to other ordinary distributions like normal. After studying the basic properties of the new class in general setting, we consider the two-sided generalized normal distribution with maximum likelihood estimation procedure. 相似文献